On distributions of diffusion processes in Hilbert spaces at a fixed moment in time

Oxana Manita

Published 2015-08-25Version 1

We consider diffusion processes in Hilbert space, corresponding to stochastic partial differential equations. We show that a non-degenerate diffusion process at any moment in time is situated in any given ellipsoid, the parameters of which are adjusted to the Wiener process, with a strictly positive probability. This is a partial infinite-dimensional analogue of the existence of a positive density (with respect to the Lebesgue measure) of the transition probability.